On the Structure of Groups Whose Non-normal Subgroups Are Core-Free
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DOI: 10.1007/s00009-019-1427-6
Abstract: A subgroup H of a group G is called core-free if \({\mathbf{Core}}_{G}(H)=\bigcap \nolimits _{x\in G}H^{x}=\langle 1\rangle \). In the current article, we study the groups in which every subgroup is either normal or core-free. read more here.
Keywords: normal subgroups; non normal; structure groups; core free ... See more keywords
Finite groups whose subgroup graph contains a vertex of large degree
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DOI: 10.1007/s00013-025-02121-1
Abstract: Burness and Scott (J Aust Math Soc 87:329-357, 2009) classified finite groups G such that the number of prime order subgroups of G is greater than |G|/2-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt}… read more here.
Keywords: subgroup graph; finite groups; graph contains; groups whose ... See more keywords
Finite groups whose noncyclic graphs have positive genus
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DOI: 10.1007/s10474-020-01033-6
Abstract: For a finite noncyclic group G , let $${\rm Cyc} (G)$$ Cyc ( G ) be a set of elements a of G such that $$\langle a, b\rangle$$ ⟨ a , b ⟩ is cyclic… read more here.
Keywords: finite noncyclic; genus; whose noncyclic; noncyclic graphs ... See more keywords
On groups all of whose Haar graphs are Cayley graphs
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DOI: 10.1007/s10801-019-00894-7
Abstract: A Cayley graph of a group H is a finite simple graph $$\Gamma $$ Γ such that $$\mathrm{Aut}(\Gamma )$$ Aut ( Γ ) contains a subgroup isomorphic to H acting regularly on $$V(\Gamma ),$$ V… read more here.
Keywords: graphs; cayley; whose haar; graph ... See more keywords
Finite groups whose n-maximal subgroups are σ-subnormal
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DOI: 10.1007/s11425-016-9211-9
Abstract: Let σ = {σi | i ∈ I} be some partition of the set of all primes P. A set H of subgroups of G is said to be a complete Hallσ-set of G if… read more here.
Keywords: finite groups; subgroup; maximal subgroup; hall ... See more keywords
Nonsolvable groups whose irreducible character degrees have special 2-parts
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DOI: 10.1007/s11464-021-0984-8
Abstract: Let G be a nonsolvable group and Irr(G) the set of irreducible complex characters of G. We consider the nonsolvable groups whose character degrees have special 2-parts and prove that if χ(1)2 = 1 or… read more here.
Keywords: character degrees; degrees special; nonsolvable groups; special parts ... See more keywords
Groups with all subgroups either modular or soluble of finite rank
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DOI: 10.1016/j.jalgebra.2020.12.005
Abstract: Abstract We study locally graded groups whose non-modular subgroups are soluble and satisfy some rank condition. In particular, in order to characterize locally graded groups whose subgroups are either modular or polycyclic, we describe (generalized)… read more here.
Keywords: modular soluble; groups subgroups; subgroups either; groups whose ... See more keywords
FINITE $p$-GROUPS ALL OF WHOSE NONNORMAL SUBGROUPS HAVE BOUNDED NORMAL CORES
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DOI: 10.1017/s0004972719000753
Abstract: Given a positive integer $m$, a finite $p$-group $G$ is called a $BC(p^{m})$-group if $|H_{G}|\leq p^{m}$ for every nonnormal subgroup $H$ of $G$, where $H_{G}$ is the normal core of $H$ in $G$. We show… read more here.
Keywords: groups whose; subgroups bounded; finite groups; nonnormal subgroups ... See more keywords
ON GROUPS WHOSE SUBGROUPS ARE EITHER MODULAR OR CONTRANORMAL
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DOI: 10.1017/s0004972721000447
Abstract: Abstract A subgroup H of a group G is said to be contranormal in G if the normal closure of H in G is equal to G. In this paper, we consider groups whose nonmodular… read more here.
Keywords: groups whose; contranormal; either modular; modular contranormal ... See more keywords
Finite p-groups all of whose proper subgroups of class 2 are metacyclic
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DOI: 10.1080/00927872.2020.1843048
Abstract: Abstract In this note, we classify finite p-groups all of whose proper subgroups of nilpotency class equal to 2 are metacyclic. read more here.
Keywords: finite groups; whose proper; subgroups class; groups whose ... See more keywords
Finite Groups Whose n-Maximal Subgroups Are Modular
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DOI: 10.1134/s0037446618030187
Abstract: Let G be a finite group. If Mn< Mn−1< · · · < M1< M0 = G with Mi a maximal subgroup of Mi−1 for all i = 1,..., n, then Mn (n > 0)… read more here.
Keywords: finite groups; subgroup; maximal subgroups; whose maximal ... See more keywords